Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
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#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;

int n;
int data[1000];

int main() {
	int i;
	
	cin >> n;
	for (i = 0; i < n; i++) cin >> data[i];
	sort(data, data + n);
	
	double maxval = 0;
	for (i = 1; i < n - 2; i++) {
		maxval = max(maxval, (double)(data[n - 1] + data[n - 2]) / (data[i] - data[i - 1]));
	}
	maxval = max(maxval, (double)(data[n - 1] + data[n - 4]) / (data[n - 2] - data[n - 3]));
	maxval = max(maxval, (double)(data[n - 3] + data[n - 4]) / (data[n - 1] - data[n - 2]));
	
	printf("%.14f\n", maxval);
	return 0;
}